TSTP Solution File: SWV014+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWV014+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 11:02:40 EDT 2023
% Result : Theorem 4.25s 2.02s
% Output : CNFRefutation 4.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 40
% Syntax : Number of formulae : 83 ( 22 unt; 26 typ; 0 def)
% Number of atoms : 128 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 128 ( 57 ~; 49 |; 13 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 20 >; 10 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-1 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-4 aty)
% Number of variables : 72 (; 71 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ t_holds > party_of_protocol > message > intruder_message > intruder_holds > fresh_to_b > b_stored > b_holds > a_stored > a_nonce > a_holds > quadruple > triple > sent > pair > key > encrypt > #nlpp > generate_key > generate_expiration_time > generate_b_nonce > t > bt > b > at > an_a_nonce > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sent,type,
sent: ( $i * $i * $i ) > $i ).
tff(b_stored,type,
b_stored: $i > $o ).
tff(fresh_to_b,type,
fresh_to_b: $i > $o ).
tff(a,type,
a: $i ).
tff(t,type,
t: $i ).
tff(encrypt,type,
encrypt: ( $i * $i ) > $i ).
tff(key,type,
key: ( $i * $i ) > $i ).
tff(b_holds,type,
b_holds: $i > $o ).
tff(an_a_nonce,type,
an_a_nonce: $i ).
tff(a_holds,type,
a_holds: $i > $o ).
tff(b,type,
b: $i ).
tff(at,type,
at: $i ).
tff(t_holds,type,
t_holds: $i > $o ).
tff(message,type,
message: $i > $o ).
tff(generate_key,type,
generate_key: $i > $i ).
tff(a_stored,type,
a_stored: $i > $o ).
tff(pair,type,
pair: ( $i * $i ) > $i ).
tff(party_of_protocol,type,
party_of_protocol: $i > $o ).
tff(triple,type,
triple: ( $i * $i * $i ) > $i ).
tff(intruder_holds,type,
intruder_holds: $i > $o ).
tff(generate_b_nonce,type,
generate_b_nonce: $i > $i ).
tff(quadruple,type,
quadruple: ( $i * $i * $i * $i ) > $i ).
tff(a_nonce,type,
a_nonce: $i > $o ).
tff(intruder_message,type,
intruder_message: $i > $o ).
tff(bt,type,
bt: $i ).
tff(generate_expiration_time,type,
generate_expiration_time: $i > $i ).
tff(f_28,axiom,
message(sent(a,b,pair(a,an_a_nonce))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_sent_message_i_to_b) ).
tff(f_71,axiom,
! [U,V,W] :
( message(sent(U,V,W))
=> intruder_message(W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_can_record) ).
tff(f_77,axiom,
! [U,V] :
( intruder_message(pair(U,V))
=> ( intruder_message(U)
& intruder_message(V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_decomposes_pairs) ).
tff(f_40,axiom,
fresh_to_b(an_a_nonce),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonce_a_is_fresh_to_b) ).
tff(f_48,axiom,
! [U,V] :
( ( message(sent(U,b,pair(U,V)))
& fresh_to_b(V) )
=> ( message(sent(b,t,triple(b,generate_b_nonce(V),encrypt(triple(U,V,generate_expiration_time(V)),bt))))
& b_stored(pair(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_creates_freash_nonces_in_time) ).
tff(f_85,axiom,
! [U,V,W] :
( intruder_message(triple(U,V,W))
=> ( intruder_message(U)
& intruder_message(V)
& intruder_message(W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_decomposes_triples) ).
tff(f_141,axiom,
! [V,W] :
( ( intruder_message(V)
& party_of_protocol(W) )
=> intruder_holds(key(V,W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_holds_key) ).
tff(f_149,axiom,
! [U,V,W] :
( ( intruder_message(U)
& intruder_holds(key(V,W))
& party_of_protocol(W) )
=> intruder_message(encrypt(U,V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_key_encrypts) ).
tff(f_39,axiom,
party_of_protocol(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_party_of_protocol) ).
tff(f_27,axiom,
party_of_protocol(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_party_of_protocol) ).
tff(f_101,axiom,
! [U,V] :
( ( intruder_message(U)
& intruder_message(V) )
=> intruder_message(pair(U,V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_composes_pairs) ).
tff(f_135,axiom,
! [U,V,W] :
( ( intruder_message(U)
& party_of_protocol(V)
& party_of_protocol(W) )
=> message(sent(V,W,U)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_message_sent) ).
tff(f_54,axiom,
! [V,X,Y] :
( ( message(sent(X,b,pair(encrypt(triple(X,V,generate_expiration_time(Y)),bt),encrypt(generate_b_nonce(Y),V))))
& b_stored(pair(X,Y)) )
=> b_holds(key(V,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_accepts_secure_session_key) ).
tff(f_162,negated_conjecture,
~ ? [U] :
( intruder_holds(key(U,b))
& b_holds(key(U,a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(c_6,plain,
message(sent(a,b,pair(a,an_a_nonce))),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_34,plain,
! [W_21,U_19,V_20] :
( intruder_message(W_21)
| ~ message(sent(U_19,V_20,W_21)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_90,plain,
intruder_message(pair(a,an_a_nonce)),
inference(resolution,[status(thm)],[c_6,c_34]) ).
tff(c_36,plain,
! [V_23,U_22] :
( intruder_message(V_23)
| ~ intruder_message(pair(U_22,V_23)) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_97,plain,
intruder_message(an_a_nonce),
inference(resolution,[status(thm)],[c_90,c_36]) ).
tff(c_18,plain,
fresh_to_b(an_a_nonce),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_210,plain,
! [V_131,U_132] :
( message(sent(b,t,triple(b,generate_b_nonce(V_131),encrypt(triple(U_132,V_131,generate_expiration_time(V_131)),bt))))
| ~ fresh_to_b(V_131)
| ~ message(sent(U_132,b,pair(U_132,V_131))) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_215,plain,
( message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))))
| ~ fresh_to_b(an_a_nonce) ),
inference(resolution,[status(thm)],[c_6,c_210]) ).
tff(c_221,plain,
message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_215]) ).
tff(c_225,plain,
intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))),
inference(resolution,[status(thm)],[c_221,c_34]) ).
tff(c_42,plain,
! [V_25,U_24,W_26] :
( intruder_message(V_25)
| ~ intruder_message(triple(U_24,V_25,W_26)) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_236,plain,
intruder_message(generate_b_nonce(an_a_nonce)),
inference(resolution,[status(thm)],[c_225,c_42]) ).
tff(c_64,plain,
! [V_46,W_47] :
( intruder_holds(key(V_46,W_47))
| ~ party_of_protocol(W_47)
| ~ intruder_message(V_46) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_143,plain,
! [U_104,V_105,W_106] :
( intruder_message(encrypt(U_104,V_105))
| ~ party_of_protocol(W_106)
| ~ intruder_holds(key(V_105,W_106))
| ~ intruder_message(U_104) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_146,plain,
! [U_104,V_46,W_47] :
( intruder_message(encrypt(U_104,V_46))
| ~ intruder_message(U_104)
| ~ party_of_protocol(W_47)
| ~ intruder_message(V_46) ),
inference(resolution,[status(thm)],[c_64,c_143]) ).
tff(c_161,plain,
! [W_47] : ~ party_of_protocol(W_47),
inference(splitLeft,[status(thm)],[c_146]) ).
tff(c_16,plain,
party_of_protocol(b),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_165,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_161,c_16]) ).
tff(c_166,plain,
! [U_104,V_46] :
( intruder_message(encrypt(U_104,V_46))
| ~ intruder_message(U_104)
| ~ intruder_message(V_46) ),
inference(splitRight,[status(thm)],[c_146]) ).
tff(c_4,plain,
party_of_protocol(a),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_147,plain,
! [U_107,V_108] :
( b_stored(pair(U_107,V_108))
| ~ fresh_to_b(V_108)
| ~ message(sent(U_107,b,pair(U_107,V_108))) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_154,plain,
( b_stored(pair(a,an_a_nonce))
| ~ fresh_to_b(an_a_nonce) ),
inference(resolution,[status(thm)],[c_6,c_147]) ).
tff(c_160,plain,
b_stored(pair(a,an_a_nonce)),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_154]) ).
tff(c_40,plain,
! [W_26,U_24,V_25] :
( intruder_message(W_26)
| ~ intruder_message(triple(U_24,V_25,W_26)) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_237,plain,
intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)),
inference(resolution,[status(thm)],[c_225,c_40]) ).
tff(c_54,plain,
! [U_31,V_32] :
( intruder_message(pair(U_31,V_32))
| ~ intruder_message(V_32)
| ~ intruder_message(U_31) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_62,plain,
! [V_44,W_45,U_43] :
( message(sent(V_44,W_45,U_43))
| ~ party_of_protocol(W_45)
| ~ party_of_protocol(V_44)
| ~ intruder_message(U_43) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_238,plain,
! [V_133,X_134,Y_135] :
( b_holds(key(V_133,X_134))
| ~ b_stored(pair(X_134,Y_135))
| ~ message(sent(X_134,b,pair(encrypt(triple(X_134,V_133,generate_expiration_time(Y_135)),bt),encrypt(generate_b_nonce(Y_135),V_133)))) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_242,plain,
! [V_133,V_44,Y_135] :
( b_holds(key(V_133,V_44))
| ~ b_stored(pair(V_44,Y_135))
| ~ party_of_protocol(b)
| ~ party_of_protocol(V_44)
| ~ intruder_message(pair(encrypt(triple(V_44,V_133,generate_expiration_time(Y_135)),bt),encrypt(generate_b_nonce(Y_135),V_133))) ),
inference(resolution,[status(thm)],[c_62,c_238]) ).
tff(c_400,plain,
! [V_176,V_177,Y_178] :
( b_holds(key(V_176,V_177))
| ~ b_stored(pair(V_177,Y_178))
| ~ party_of_protocol(V_177)
| ~ intruder_message(pair(encrypt(triple(V_177,V_176,generate_expiration_time(Y_178)),bt),encrypt(generate_b_nonce(Y_178),V_176))) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_242]) ).
tff(c_405,plain,
! [V_179,V_180,Y_181] :
( b_holds(key(V_179,V_180))
| ~ b_stored(pair(V_180,Y_181))
| ~ party_of_protocol(V_180)
| ~ intruder_message(encrypt(generate_b_nonce(Y_181),V_179))
| ~ intruder_message(encrypt(triple(V_180,V_179,generate_expiration_time(Y_181)),bt)) ),
inference(resolution,[status(thm)],[c_54,c_400]) ).
tff(c_411,plain,
( b_holds(key(an_a_nonce,a))
| ~ b_stored(pair(a,an_a_nonce))
| ~ party_of_protocol(a)
| ~ intruder_message(encrypt(generate_b_nonce(an_a_nonce),an_a_nonce)) ),
inference(resolution,[status(thm)],[c_237,c_405]) ).
tff(c_418,plain,
( b_holds(key(an_a_nonce,a))
| ~ intruder_message(encrypt(generate_b_nonce(an_a_nonce),an_a_nonce)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_160,c_411]) ).
tff(c_420,plain,
~ intruder_message(encrypt(generate_b_nonce(an_a_nonce),an_a_nonce)),
inference(splitLeft,[status(thm)],[c_418]) ).
tff(c_423,plain,
( ~ intruder_message(generate_b_nonce(an_a_nonce))
| ~ intruder_message(an_a_nonce) ),
inference(resolution,[status(thm)],[c_166,c_420]) ).
tff(c_427,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_97,c_236,c_423]) ).
tff(c_428,plain,
b_holds(key(an_a_nonce,a)),
inference(splitRight,[status(thm)],[c_418]) ).
tff(c_99,plain,
! [V_74,W_75] :
( intruder_holds(key(V_74,W_75))
| ~ party_of_protocol(W_75)
| ~ intruder_message(V_74) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_76,plain,
! [U_53] :
( ~ b_holds(key(U_53,a))
| ~ intruder_holds(key(U_53,b)) ),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_103,plain,
! [V_74] :
( ~ b_holds(key(V_74,a))
| ~ party_of_protocol(b)
| ~ intruder_message(V_74) ),
inference(resolution,[status(thm)],[c_99,c_76]) ).
tff(c_106,plain,
! [V_74] :
( ~ b_holds(key(V_74,a))
| ~ intruder_message(V_74) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_103]) ).
tff(c_432,plain,
~ intruder_message(an_a_nonce),
inference(resolution,[status(thm)],[c_428,c_106]) ).
tff(c_436,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_97,c_432]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV014+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 23:06:59 EDT 2023
% 0.14/0.36 % CPUTime :
% 4.25/2.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.25/2.03
% 4.25/2.03 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.25/2.06
% 4.25/2.06 Inference rules
% 4.25/2.06 ----------------------
% 4.25/2.06 #Ref : 0
% 4.25/2.06 #Sup : 53
% 4.25/2.06 #Fact : 0
% 4.25/2.06 #Define : 0
% 4.25/2.06 #Split : 6
% 4.25/2.06 #Chain : 0
% 4.25/2.06 #Close : 0
% 4.25/2.06
% 4.25/2.06 Ordering : KBO
% 4.25/2.06
% 4.25/2.06 Simplification rules
% 4.25/2.06 ----------------------
% 4.25/2.06 #Subsume : 47
% 4.25/2.06 #Demod : 33
% 4.25/2.06 #Tautology : 14
% 4.25/2.06 #SimpNegUnit : 49
% 4.25/2.06 #BackRed : 19
% 4.25/2.06
% 4.25/2.06 #Partial instantiations: 0
% 4.25/2.07 #Strategies tried : 1
% 4.25/2.07
% 4.25/2.07 Timing (in seconds)
% 4.25/2.07 ----------------------
% 4.25/2.07 Preprocessing : 0.56
% 4.25/2.07 Parsing : 0.33
% 4.25/2.07 CNF conversion : 0.03
% 4.25/2.07 Main loop : 0.43
% 4.25/2.07 Inferencing : 0.17
% 4.25/2.07 Reduction : 0.12
% 4.25/2.07 Demodulation : 0.08
% 4.25/2.07 BG Simplification : 0.02
% 4.25/2.07 Subsumption : 0.09
% 4.25/2.07 Abstraction : 0.01
% 4.25/2.07 MUC search : 0.00
% 4.25/2.07 Cooper : 0.00
% 4.25/2.07 Total : 1.05
% 4.25/2.07 Index Insertion : 0.00
% 4.25/2.07 Index Deletion : 0.00
% 4.25/2.07 Index Matching : 0.00
% 4.25/2.07 BG Taut test : 0.00
%------------------------------------------------------------------------------